Please help me to solve this simple error

%Code
% Tanh–Coth Method for Solving Nonlinear ODEs
clear; clc; syms U(xi) a0 a1 a2 b1 b2 c xi d1 d2 d3

% Example ODE: U'' - U + 2*U^3 = 0
ode = diff(U, xi, 2)*U^2 +(diff(U, xi, 1))^2*(2*U+1)+d1*U^4+d2*U^3;

% Step 1: Assume tanh–coth solution (up to order 2 for example)
U_trial = a0 + a1*tanh(d3*xi) + a2*tanh(d3*xi)^2 + b1*coth(d3*xi) + b2*coth(d3*xi)^2;

% Step 2: Substitute the trial function into the ODE
ode_sub = subs(ode, U, U_trial);

% Step 3: Expand and simplify
ode_simplified = simplify(expand(ode_sub));

% Step 4: Collect terms with respect to tanh and coth
% Convert to polynomial form in tanh(xi) and coth(xi)
ode_collected = collect(ode_simplified, [tanh(d3*xi), coth(d3*xi)]);

% Step 5: Equate coefficients of each power of tanh and coth to zero
% (To make the equation identically zero)
coeffs_tanh = coeffs(ode_collected, tanh(xi));
eqns = [];
for k = 1:length(coeffs_tanh)
    eqns = [eqns, simplify(coeffs_tanh(k)) == 0];
end

% Step 6: Solve for coefficients
sol = solve(eqns, [a0 a1 a2 b1 b2 d1 d2 d3], 'IgnoreAnalyticConstraints', true);

disp('Solutions for coefficients:')
disp(sol)

Answer 1

[Walter Roberson]

You have an installation error; somehow the implementing function (class actually) for sym has become a script instead of a function. You will need to reinstall the Symbolic Toolbox.

Your ode contains a single function, so eqns ends up containing a single equation. But you try to solve() that equation for 8 variables. solve() ends up hunting for degenerate solutions, combinations of variables that solve the entire equation at the same time; that takes a long time and is unlikely to succeed.

[Tarek]

Thank you

Answer 2

[Torsten]

@Walter Roberson answered the question about your MATLAB error.

Concerning the problem you try to solve:

I assume d1, d2 are not equal to 0.

"ode_sub" is a polynomial in tanh(d3*xi) and coth(d3*xi) of degree 8. In order to make it satisfy the ode, you will have to find a0 a1 a2 b1 b2 d3 such that 16 coefficients (8 in front of tanh(d3*xi) and 8 in front of coth(d3*xi)) become 0. Thus you have a system of 16 equations in 6 free parameters. The system is overdetermined - there will hardly be a solution.

Of course, U identically 0 (thus a0 a1 a2 b1 b2 all equal to 0) solves the ode. But I doubt this is a solution you are looking for.

[Tarek]

Thank you